Graphical perception and cognition
Objectives
- Define elementary perceptual tasks
- Review hierarchy of perceptual tasks and how this was developed
- Design experiments to test theories of percepual tasks and Tufte’s data-ink ratio
library(tidyverse)
library(ggthemes)## Warning: package 'ggthemes' was built under R version 3.4.4library(knitr)
library(broom)
library(stringr)
library(lubridate)
options(digits = 3)
set.seed(1234)
theme_set(theme_minimal())theme_void2 <- function (base_size = 11, base_family = "", base_line_size = base_size/22,
base_rect_size = base_size/22) {
half_line <- base_size/2
theme(line = element_blank(),
rect = element_blank(),
text = element_text(family = base_family,
face = "plain",
colour = "black",
size = base_size,
lineheight = 0.9,
hjust = 0.5,
vjust = 0.5,
angle = 0,
margin = margin(), debug = FALSE),
axis.text.y = element_blank(),
axis.title = element_blank(),
axis.ticks.length = unit(0, "pt"),
legend.key.size = unit(1.2, "lines"),
legend.position = "right",
legend.text = element_text(size = rel(0.8)),
legend.title = element_text(hjust = 0),
strip.text = element_text(size = rel(0.8)),
strip.switch.pad.grid = unit(0.1, "cm"),
strip.switch.pad.wrap = unit(0.1, "cm"),
panel.ontop = FALSE,
panel.spacing = unit(half_line, "pt"),
plot.margin = unit(c(0, 0, 0, 0), "lines"),
plot.title = element_text(size = rel(1.2), hjust = 0,
vjust = 1, margin = margin(t = half_line * 1.2)),
plot.subtitle = element_text(size = rel(0.9), hjust = 0,
vjust = 1, margin = margin(t = half_line * 0.9)),
plot.caption = element_text(size = rel(0.9), hjust = 1,
vjust = 1, margin = margin(t = half_line * 0.9)),
complete = TRUE)
}Cleveland and McGill
- What makes a graph more accurate?
A graphical form that involves elementary perceptual tasks that lead to more accurate judgments than another graphical form (with the same quantitiative information) will result in better organization and increase the chances of a correct perception of patterns and behavior.
Figure 6.12 from The Functional Art
- Discuss - what other metrics should we consider? Is this always the outcome we should care about?
- Observing patterns
- Identifying trends/relationships
- What else?
Basic perceptual tasks on graphs
Bar chart
diamonds_sum <- diamonds %>%
group_by(cut) %>%
summarize(n = n()) %>%
ungroup %>%
mutate(pct = n / sum(n))
ggplot(diamonds_sum, aes(cut, pct)) +
geom_col() +
scale_y_continuous(labels = scales::percent) +
labs(title = "Diamonds data",
x = "Cut of diamond",
y = "Percentage of sample")
Pie chart
ggplot(diamonds_sum, aes(x = factor(1), y = pct, fill = cut)) +
geom_col(width = 1) +
coord_polar(theta = "y", direction = -1) +
theme_void()
Statistical maps with color
library(fiftystater)
data("fifty_states") # this line is optional due to lazy data loading
crimes <- data.frame(state = tolower(rownames(USArrests)), USArrests)
# map_id creates the aesthetic mapping to the state name column in your data
p <- ggplot(crimes, aes(map_id = state)) +
# map points to the fifty_states shape data
geom_map(aes(fill = Assault), map = fifty_states) +
expand_limits(x = fifty_states$long, y = fifty_states$lat) +
coord_map() +
scale_x_continuous(breaks = NULL) +
scale_y_continuous(breaks = NULL) +
labs(title = "Assaults per 100,000 residents in 1973",
x = NULL,
y = NULL) +
theme(legend.position = "bottom",
panel.background = element_blank()) +
fifty_states_inset_boxes()
# default colors
p
Fix the area as constant
library(statebins)
USArrests %>%
rownames_to_column("State") %>%
statebins(state_col = "State",
value_col = "Assault") +
labs(title = "Assaults per 100,000 residents in 1973",
x = NULL,
y = NULL) +
theme_statebins()
Scatterplot
# generate correlated data
xy <- ecodist::corgen(len = 20, r = .95) %>%
bind_cols
ggplot(xy, aes(x, y)) +
geom_point()
xy %>%
mutate(id = row_number()) %>%
gather(var, value, -id) %>%
ggplot(aes(id, value, fill = var)) +
geom_col(position = "dodge")
Curvature
polls <- read_csv("https://projects.fivethirtyeight.com/trump-approval-data/approval_polllist.csv")## Parsed with column specification:
## cols(
## .default = col_character(),
## samplesize = col_integer(),
## weight = col_double(),
## influence = col_integer(),
## approve = col_double(),
## disapprove = col_double(),
## adjusted_approve = col_double(),
## adjusted_disapprove = col_double(),
## tracking = col_logical(),
## poll_id = col_integer(),
## question_id = col_integer()
## )## See spec(...) for full column specifications.## Warning in rbind(names(probs), probs_f): number of columns of result is not
## a multiple of vector length (arg 1)## Warning: 210 parsing failures.
## row # A tibble: 5 x 5 col row col expected actual file expected <int> <chr> <chr> <chr> <chr> actual 1 1546 influence an integer .0013319 'https://projects.fivethirtyeight.c… file 2 1547 influence an integer .0056207 'https://projects.fivethirtyeight.c… row 3 1548 influence an integer .0051985 'https://projects.fivethirtyeight.c… col 4 1549 influence an integer .0009761 'https://projects.fivethirtyeight.c… expected 5 1550 influence an integer .0025643 'https://projects.fivethirtyeight.c…
## ... ................. ... .......................................................................... ........ .......................................................................... ...... .......................................................................... .... .......................................................................... ... .......................................................................... ... .......................................................................... ........ ..........................................................................
## See problems(...) for more details.polls_data <- polls %>%
filter(subgroup == "All polls") %>%
select(enddate, adjusted_approve, adjusted_disapprove) %>%
mutate(date = mdy(enddate))
polls_data %>%
gather(var, value, starts_with("adjusted")) %>%
mutate(var = factor(var, levels = c("adjusted_approve", "adjusted_disapprove"),
labels = c("Approve", "Disapprove")),
value = value / 100) %>%
ggplot(aes(date, value, color = var)) +
geom_smooth() +
scale_y_continuous(label = scales::percent) +
labs(title = "How popular/unpopular is Donald Trump?",
x = NULL,
y = NULL,
color = NULL,
caption = "Source: FiveThirtyEight") +
theme(legend.position = "bottom")## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
polls_data %>%
mutate(diff = (adjusted_approve - adjusted_disapprove) / 100) %>%
ggplot(aes(date, diff)) +
geom_hline(yintercept = 0) +
geom_smooth() +
scale_y_continuous(label = scales::percent) +
labs(title = "How popular/unpopular is Donald Trump?",
x = NULL,
y = "Net approval rating",
caption = "Source: FiveThirtyEight")## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Experimental design
- \(N = 55\)
- Used bar charts and pie charts
- Experiment 1 - asked to make assessments of length and position along a common scale
- Experiment 2 - asked to make judgments of position and angle (pie vs bar chart)
- Make visual assessments of what percentage one value was of a larger value
- \(\log_2 (\mid \text{judged percent} - \text{true percent} \mid + \frac{1}{8})\)
Cairo - applying perceptual task scale
A screenshot of data. Source: The Functional Art
A proportional symbol map. Source: The Functional Art
Chloropeth map. Source: The Functional Art
Dot chart. Source: The Functional Art
Scatterplot. Source: The Functional Art
Slopegraph. Source: The Functional Art
What we learn
- Use theory and experiments to develop rules for data visualization (not Tufte’s assertion approach)
- Different perceptual tasks (i.e. different channels) are easier or harder to decode and accurately interpret
- Pick the highest-level encoding task possible given the data structure/purpose of the visualization
Crowdsourcing Graphical Perception
Transparency of gridlines
- Recall that Tufte hates gridlines
- Experiment 2 crowdsources the optimal transparency for the gridlines and data points in a scatterplot
ggplot(mpg, aes(cty, hwy)) +
geom_point()
ggplot(mpg, aes(cty, hwy)) +
geom_point() +
theme(panel.grid.major = element_line("grey70"),
panel.grid.minor = element_line("grey70"))
ggplot(mpg, aes(cty, hwy)) +
geom_point() +
theme(panel.grid.major = element_line("grey50"),
panel.grid.minor = element_line("grey50"))
ggplot(mpg, aes(cty, hwy)) +
geom_point() +
theme(panel.grid.major = element_line("grey20"),
panel.grid.minor = element_line("grey20"))
- Individuals prefer lighter (more transparent backgrounds)
- Could be run using a Shiny app integrated into an MTurk experiment
In defense of pie charts
- Which is easier to distinguish: line length or area, angle, and arc length?
Psychophysical theory of perception. Function of relationship between perceived areas of circles and their physical areas
\[\text{Subjective area} = \text{Area}^.86\]
- People misjudge/misestimate area
- This function is not derived from rigorous science
- Focus more on the subarea (area/size of individual slices rather than the entire circle)
- People also do not generally use pie charts to estimate precise magnitudes (if so, use a table instead)
pie <- data_frame(label = c("A", "B", "C", "D"),
value = c(10, 20, 40, 30))
# bar chart
ggplot(pie, aes(label, value)) +
geom_col(color = "black", fill = "white") +
theme_void2()
# proportional area chart
pie_prop <- pie %>%
mutate(ymin = 0,
ymax = 1,
xmax = cumsum(value),
xmin = xmax - value,
x = (xmax - xmin) / 2 + xmin)
ggplot(pie_prop, aes(xmin = xmin, xmax = xmax,
ymin = ymin, ymax = ymax)) +
geom_rect(fill = "white", color = "black") +
scale_x_continuous(breaks = pie_prop$x, labels = pie_prop$label) +
theme_void2()
# pie chart
ggplot(pie, aes(x = factor(1), y = value)) +
geom_col(width = 1, color = "black", fill = "white") +
geom_text(aes(label = label), position = position_stack(vjust = .5), size = 4) +
coord_polar(theta = "y", direction = 1) +
theme_void() +
theme(legend.position = "none")
# table
pie %>%
select(value) %>%
t %>%
knitr::kable(col.names = pie$label,
row.names = FALSE)| A | B | C | D |
|---|---|---|---|
| 10 | 20 | 40 | 30 |
Experiment 1
- Compare speed at processing and making comparisons between bar charts and pie charts
- No substantial difference in processing time or accuracy of interpretations - see Figures 2 and 3
Experiment 2
- Ordering of the bars/slices didn’t really effect interpretation speed or accuracy - ordering apparently is not a major perceptual strategy
Experiment 3
- Pie charts better for A + B vs. C + D comparisons
- Hypothesis: in pie charts, adjacent slices were easier to visually combine together
- In truth, this didn’t matter - but for bar charts, adjacency actually helped
Takeaways
- For pure magnitude identification, bar charts are superior
- For comparing percentages, either chart is acceptable
- To compare combinations of groupings, pie charts are slightly superior
- Tables are only useful if you want to report exact percentages
Design a data visualization experiment
- Work with someone next to you (or a group of three)
- Develop a research question applicable to visual design that can be answered experimentally
- Replicate something from Cleveland and McGill
- Extend to additional question
- Tufte minimalism
- How will you design two (or more) graphs to obtain an accurate and unbiased estimate?
Session Info
devtools::session_info()## Session info -------------------------------------------------------------## setting value
## version R version 3.4.3 (2017-11-30)
## system x86_64, darwin15.6.0
## ui X11
## language (EN)
## collate en_US.UTF-8
## tz America/Chicago
## date 2018-04-17## Packages -----------------------------------------------------------------## package * version date source
## assertthat 0.2.0 2017-04-11 CRAN (R 3.4.0)
## backports 1.1.2 2017-12-13 CRAN (R 3.4.3)
## base * 3.4.3 2017-12-07 local
## bindr 0.1.1 2018-03-13 CRAN (R 3.4.3)
## bindrcpp 0.2.2.9000 2018-04-08 Github (krlmlr/bindrcpp@bd5ae73)
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